Speaker
Masamichi Miyaji
Description
In this talk, I will present a path-integral derivation of the Hilbert space of Jackiw–Teitelboim (JT) gravity in closed universes, in both de Sitter and anti-de Sitter spacetime. Through a careful analysis of the gravitational path integral, we evaluate the inner products exactly and show that the physical Hilbert space is naturally described as a space of coinvariant states equipped with a group-averaged inner product. Our results also have implications for the path-integral measure in configuration space. Furthermore, we propose a nonperturbative completion of this model that incorporates topology-changing processes and possesses a nontrivial finite-dimensional Hilbert space.